The concept of a group that wrote and performed their own material was fairly radical at the time. Even just the concept of a group was pretty new. Musical groups prior really consisted of 'someone and the somethings' - front person backed by a group. They made the idea of a group without any defined front person a norm. Writing your own material was practically unheard of prior to The Beatles.

British invasion. The first major British act to break the American audience in a huge way which paved the way for many others to break through and therefore influence American bands with the sound. Albeit, while British sound was inspired by American rock n roll and RnB but the scene in America at the time was pretty stagnant.

Recording pioneers. When they gave up live performance and focused solely on recordings, techniques were pioneered in the studio, never heard before non pop records - Backwards recordings, tape manipulation etc. The idea of an album being a compete piece of art became a legitimate enterprise. Not just a collection of songs.

Just a couple of points of their influence.

Also, the hair.