The mode is the most frequent value of a set of numbers.
Example: The mode of {1,2,3,3,3,3,3,4,5} is 3 since it shows up the most.
It's strongly recommended to sort the values before looking for the mode. Also, I recommend making a frequency chart to spot the mode easier.
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It is possible for a set to have more than one mode.
For example, the set {1,1,2,3,3,4,5} has the mode {1,3} because both 1 and 3 show up the most. They are tied for the most frequent. Basically we're saying "both 1 and 3 are the mode". It's a bit misleading since "the mode" implies there's one value, when clearly there could be more than one value.
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It is possible for a set to have no mode at all.
Example: {1,2,3,4,5} has no mode. Each value shows up exactly once. No value shows up more than that, so we don't have "most frequent". It might be tempting to say "The mode is {1,2,3,4,5}" and follow the template mentioned in the 2nd section, but that's not what happens. We simply say "no mode" and move on. The 2nd section works because those two values show up more than the others. There has to be a clear edge.
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The mode is a strange concept because we could have 1 mode, multiple modes, or none at all. This doesn't happen with any other value such as mean or median (each of which has exactly one value only).