The fluid mosaic model describes the composition and function of cell membranes. Membranes are made of lipids and proteins (and a few other bits and bobs but don’t worry about that here). The lipids and proteins form a double layer sheet but they do not form strong bonds between themselves. They stick together because they have hydrophobic tails which try to get away from the surrounding cytosol, so they bury themselves in the middle of the double layer. They also have hydrophilic heads which stand up towards the cytosol. The all stand up like a group of penguins; not stuck together directly but huddling together so that the hydrophilic tails are all hidden from the cytosol.
When viewed from above, they look like a mosaic. Because they are not directly stuck together they can move freely within the double layer, ie forwards, backwards and side to side, but staying within the double layer. Individual proteins and lipids can move around, therefore it can be said to be fluid.