Everything on the internet is squares, so grid based design is using a grid to determine where those squares are placed relative to each other.
Responsive webpages are ones built to display properly on a variety of screen sizes, which is important because more people are accessing the web on phones and tablets, which have smaller screens.
The materials we have studied haven't used this term, but it appears that semantic structure refers to the use of HTML tags that describe specific elements of a website, for example <header> which defines the header, or <em>, which shows the text within is emphasized.