Let's say you take the pollen of tomato variety A (the donor) and transfer it to the stamen of tomato variety B (the recipient). The fruit from that particular blossom on variety B will be a crossed tomato. When that tomato ripens, it will look exactly the same as the other tomatoes on plant B, but the seeds will different -- they contain DNA from variety A and variety B.
When you save and grow those F1 seeds, you will then see the result of crossing A and B. You will see desirable traits of variety A and variety B show up in this HYBRID plant.
What gets interesting is if you save seeds out of those tomatoes grown from that hybrid plant and grow them the next year, because those will be F2 or (filial generation 2), and you can see some huge differences. For instance, if plant A was an orange tomato and plant B was a purple tomato, then in F2, you might get reds, pinks, oranges, purples, different leaf types, etc. etc.
Seed companies have workers in 3rd world countries grow and cross 2 different tomato plants every few years to get enough "crossed" fruits to get enough seeds to fill those seed packets of Big Boy, Big Beef, Celebrity, etc.
http://en.wikipedia.org/wiki/F1_hybrid