# Why do you look ... brother's eye, but you do not take notice of the log that is in your own eye?

"You look ... brother's eye, but you do not notice the log that is in your own eye." or "Do not look ... brother's eye and ignore the log that is in your own eye." 

# the tiny piece of straw that is in your brother's eye

This refers to the less important faults of a fellow believer. 

# tiny piece of straw

"speck" or "splinter" or "bit of dust." Use a word for the smallest thing that commonly falls into a person's eyes.

# brother

All occurrences of "brother" in 7:3-5 refer to a fellow believer, not to a literal brother or a neighbor.

# the log that is in your own eye

This is refers to a person's serious faults. Jesus is saying that a person should pay attention to his own serious faults before he deals with another person's less important faults. 

# log

the largest part of a tree that someone has cut down