Also see the "What do I need to know no matter what language I use?" section!
Compiler – A compiler is a program that reads the program you have written (the "code") and translates it according to the language specs into an executable program.
Databse – A database is a file that holds information in a structured way, in some respects similiar to a spreadsheet. They are often used in programming to store data and to retrieve that data back for use by the program.
Algorithm – An algorithm is a set of instructions or steps used to solve a problem. If someone asked you how to do something, and you told them to "do this, then this, then this, and if you see this do this" you have just given them an algorithm. Programs use algorithms to get results based on data.
Object Oriented – Object Oriented Programming (OOP) is a recent trend in programming languages. OOP is a redesign of how programmers think about solving problems - instead of using a function and algortihm approach, you think of the "objects" in the program and what they need to do. Don't worry too much about OOP concepts as a beginner. When it is time for you to learn them it will be obvious, and in some cases you may never have to.
Platform – Platform refers to the type of hardware and Opeating System you are creating software for. For example, Intel and Windows, or Mac and Mac OS.