I am new to gardening as I have just bought my first house

The grass is my lawn is becoming brawn/yellower every day even though I have been watering it almost every day or two and mowing it every week. I took some pictures of it this morning after mowed it:
https://imgur.com/3W1a5
https://imgur.com/PvkhY
https://imgur.com/B63AW
the right side of the first picture has some very green grass that is my neighbors (there is no fence between us). I wonder why the grass start becoming brown exactly beginig from the border with neighbors grass?
I appreciate your help
Alex