It means to suggest something in a sly or gradual way.
Try insulate, ingratiate, appreciate, repudiate, validate, implicate, navigate, and celebrate.
He insinuated that he was prepared to handle the responsibilities of having his own car.
"That's an interesting coat," the husband insinuated, without letting his wife know how ugly the coat really was.
The speaker would often insinuate alternative meanings in his speech.