LINQ:
LINQ (Language Integrated Query) is uniform query syntax in C# and VB.Net to save and retrieve data from different sources. It is integrated in C# or VB, thereby eliminating the impedance mismatch between programming languages and databases, as well as providing a single querying interface for different types of data sources.
For example, SQL is a Structured Query Language to save and retrieve data from the database the same way LINQ is a structured query syntax built in C# and VB.Net to save and retrieve data from different types of data sources like an Object Collection, an SQL server database, XML, a web service etc.
Learn LINQ step by step in LINQ tutorials section.
Lamda expression:
C# 3.0/.Net 3.5 introduced lamda expression along with LINQ. Lambda expression is a shorter way of representing anonymous method using some special syntax.
Learn lamda expression in detail in LINQ tutorials section.