A solecism is a grammatical mistake or nonstandard usage in speech or writing, such as a misplaced modifier or incorrect verb tense.

Simply put, it's a mistake.

Some are easy to detect.

‘Me and him went to the store.'

Others are more subtle.

“He's the one that stole my lunch”

should be “He's the one WHO stole my lunch.”

“I hope she'll respond back”

is redundant. It should be “I hope she'll respond” unless you already responded to her and you're hoping she'll respond back.

I heard a speaker ask the audience:

“Does that resignate with you?”

He meant “resonate.” To “resignate” means to compel someone to quit.

Occasional solecisms will usually be overlooked in casual conversation, but frequent grammatical errors in professional settings will undermine your credibility and distract from your message.