Any time you're playing a song, you're playing it in a key. There are 12 different keys, and any song can be played in any of the 12 keys. A ukulele is capable of playing in any of the keys, however, some keys are easier than others on the ukulele. Some keys are more difficult to play in. The three chords you have been working with so far in the basic ukulele lessons are the three most important chords in the key of "C".
Most songs in the key of "C" begin with the "C" chord. It is useful to know some of the names that other musicians use to describe this. Some would say that the "C" chord is the root chord in the key of "C". Others, particularily in the country music field, would refer to this as the One.
The "F" chord is known as the Four in the key of "C". Lots of songs, after starting on the One, move to the Four. Try playing some "C"'s, and then move to the "F". It almost seem as if that's where it wants to go. If you can learn to think of that relationship as moving from the One to the Four, it will really help you learning new songs and playing with other musicians.
The "G7" chord is known as the Five in the key of "C". The move from the Five to the One is the other major move that appears in almost every song. (In many ways, they are two examples of the same move... but more about that later.) Play some G7's, and get used to how the chord wants to go back to the One.