According to wiki, an electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte or a vacuum). Examples of electrodes are the cathode and anode.

Given this definition, does this mean that every electric component that has electrodes (i.e. anode or cathode), is a nonmetallic part? And what exactly is the use of an electrode? Is it just used to indicate polarity? Are there other types besides anode or cathode? Can I use electrode as a synonym for pole? I hope someone can explain this without getting too technical.

Given this definition, does this mean that every electric component that has electrodes (i.e. anode or cathode), is a nonmetallic part?

Under that definition, in order to have electrodes a component must have nonmetallic parts. But it can't be entirely non-metallic since the electrodes are part of the component and they are metal. For example, a vacuum tube is generally made from metal, glass, and empty space (vacuum). It has both metallic and non-metallic components.

And what exactly is the use of an electrode? Is it just used to indicate polarity?

The electrodes are typically the path for current to flow in and out of the component. The exact metal used might have an effect on the performance of the part, for example in a Schottky diode.

The name of the electrode depends on the polarity: the electrode where current flows in to the component is called the anode and the electrode where current flows out is called the cathode. In the case of zener diodes, these definitions are somewhat abused.

Are there other types besides anode or cathode?

A device with more than two electrodes (for example a transistor or a triode, tetrode, or pentode vacuum tube) necessarily has electrodes that aren't called the anode or cathode.

In vacuum tubes, there's typically an anode, a cathode, and one or more grid electrodes.

In a transistor there is no anode or cathode, just base, emitter, and collector for BJTs, or gate, drain, and source for MOSFETs.

Can I use electrode as a synonym for pole?

I'm not aware of any case where that would make sense. We normally talk about magnets having poles, and electronic devices having electrodes, terminals, pins, pads, contacts, leads, etc.

if the electrode is dependent on the path for current to flow in and out of the component, then does that mean the cathode could switch terminals of a component if the current is reversed?

In principle, this is true. In practice, we choose one terminal of a device to call the cathode and one to call the anode, based on the "normal" use conditions, and we don't change the names when the current direction changes. In the case of zener diodes, we even name the cathode and anode according to what they would be if the part were a rectifier diode, but we normally use a zener with current flowing in to the terminal we call the "cathode".

 
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    Great answer. I thought polarity was used in electronic devices as well? I consider polarity to be the positive and negative pole, i.e. a positive pole has alot of positive charges. (How) is that directly related to magnets? I don't see the difference between a positive/negative pole and an anode/cathode. Also, if the electrode is dependent on the path for current to flow in and out of the component, then does that mean the cathode could switch terminals of a component if the current is reversed? If true, then does that imply it's wrong that the side of the triangle of a diode is the anode? 
  • We talk about the polarity of the component, but we still don't say the component has poles. 
     
    Can we say a voltage source e.g. a cell, has electrodes? Or are electrodes only used for other polarized components? 
     
    Dry and wet cells have electrodes. A turbine generator probably doesn't.
     

Let's talk about some common electrodes that are not part of a component just to round things out. You have probably seen those fancy bathroom scales that are supposed to tell you how much fat you have. The plates on top, they are electrodes. A simple project often used to start teaching children about electronics is a basic flood level detector. It uses two electrodes to detect the presence of water. Electrostimulation therapy uses electrodes (often with adhesive). A Van de Graaff generator is an electrode. A ground rod is an electrode (as is the cold water pipe and building steel). It could be argued that an antenna is an electrode (although no one calls them that). I'm sure that I've missed some common ones, but you will notice that many electrodes are nonpolar.

nonpolar electrodes? doesn't that contradict Photon's answer? 
 
No, they are A.C. or reversible. Reversible electrodes are D.C. but can be wired either way without affecting the circuit. For example the water sensor uses the electrodes as a crude switch.
The term "electrode" is typically only used to describe connections to objects or materials that aren't part of a typical electrical circuit. For instance, the rods used in an arc welder are called "electrodes"; so are the sticky pads used in an EKG.

The terms "anode" and "cathode" have a more general usage; they are also used to describe the positive and negative terminals of solid-state components (such as LEDs), of vacuum tubes (including special types like vacuum fluorescent displays), and of batteries.

Keep in mind that, while both the general term "electrode" and the specific terms "anode" and "cathode" may have definitions which appear to be more general than what I'm describing, they are not often used that way. Referring to a pin on an IC as an "electrode", for instance, will just confuse people.