The concept behind Yoshi is solid but the execution is not quite there.
Gameplay is centered around four kinds of falling monsters, which don't actually do anything but fall and could be replaced w/ gemstones or colored bricks w/o affecting anything. The monsters drop two and occasionally three at a time into four columns. Your goal is to match up two monsters in a column, which causes them to disappear earning you points. Additionally, there are Yoshi egg halves that fall. A bottom half can be completed into a full Yoshi egg by dropping a top half on top of it. You get additional points for having monsters stacked in between egg halves which is what gives you incentive to let things stack up a little bit, which is similar to building up a four-line Tetris in Tetris. The major difference between Yoshi and most falling-blocks games though is you don't actually move the monsters that are falling but the ones that are already stacked.
This is an interesting wrinkle in gameplay and it's simple and effective enough to be fun for a while but some issues crop up with the control scheme which just get to be annoying over time. For starters, you swap columns by moving a Mario sprite underneath the playing area and pressing A or B. This works fine but the playing area is altogether too small to really use a long term strategy on this. By the the time you have monsters stacked halfway up, which is only about four deep, it becomes impossible to do the more than two column swaps before the next two monsters land simply due to having to move Mario back and forth in order to swap columns. It would be better to either have a deeper playing area--which would necessitate smaller monster sprites--or simply map each possible column swap to its own button in order to facilitate faster switching. (There are three so you'd have to use either the d-pad direction, start or select on a NES gamepad, which is less than ideal.) As it is, Yoshi is fun at first but ultimately there is not a lot of wiggle room for mistakes when going for a high score so you wind up having to use a conservative strategy which makes things feel very repetitive quickly.
If you are just dying to play a new falling-blocks game, Yoshi might hold your interest for a little bit but, really, there are just much better options for this sort of thing on NES, which has at least two (count 'em!) good versions of the original Tetris along w/ Dr. Mario and Tetris 2. Otherwise, I just don't see any interest in picking up this for anyone but Nintendo or Yoshi collectors.