Based on what I understanded in US, it is a Tax/HR term. In general, a company hires employee in 2 forms:
1) Full Time Employee, who will receive a W-2 form at end of year
2) Consultant, also called Independent Contractor, who will receive a 1099 form.
You're thinking of a contractor. A consultant can be a contractor, but doesn't have to be. Generally, consultants tend to be brought in for higher-level business issues.
-- A consultant makes recommendations and find ways to improve the processes and solve technical & business issues. You can also say that he/she is an expert in a particular field.
-- A consultant can be on a contract basis or full-time basis. In general, they are brought-in on a contract basis as they could be very expensive.
-- Consultants also bring a different perspective to look at things differently.