Basically a Hard Inquiry is where a creditor pulls your credit, and codes the inquiry in such a way that it shows on your credit report that an inquiry was done by a creditor, for the purpose of extending credit. A hard inquiry is generally not favorable, because depending on the persons credit profile it will hurt the score for about a year, but remain visible for two years. The more hard inquiries a person has, no bueno. A Soft Inquiry is also where a creditor pulls your credit, but they code it in such a way that it only shows on the report as visible to you and has no impact on credit score at all. Creditors that pull your credit in the future do not see these.
Usually when new credit is extended, it is typically a hard inquiry. Soft inquiries are very typical by your current creditors to make sure there are no issues. As an example, it is not uncommon for credit card companies to do soft inquires on people quite often to see how much debt someone has and payment history on other accounts.