Simply put, Cross means solving the cross on any side of the cube with the edge pieces matching the color of the centers on all 4 other sides. F2L stands for "First two layers". What this means is inserting the "corner" pieces of the face with a solved cross along with the edge piece that goes along with it in the corrrect orientation too.
While solving a cross is done completely intuitively, there are several tips to solve the cross faster and more efficiently. Such as:
The way to solve F2L is also mainly done intuitively, but there are algorithms that can be learned instead to solve F2L. A PDF of those algorithms can be found here. They are shown with a picture of that particular case and their algorithm in Cube notation.
This video shows how to solve an efficient cross
This video shows how to solve F2L.
The rest of the website will go over the parts of the CFOP method. The CFOP method stands for : Cross, F2L, OLL, and PLL. The home page can be found here.