Expressions and Query work in similar ways. I referred to them in an earlier post but I'm trying to cover it here. Expressions are represented as trees. Expression trees are immutable. If you want to modify the expression tree, you can construct a new expression tree by copying the existing ones and replacing nodes. You can nest expressions and define the precedence based on the structure of the tree. Different parts of the tree can be tagged so that they can be processed differently. The leaves of the trees are usually the constants or null representing the data on which expression tree evaluates. There are around 45 expression tree types that can be a node in the tree. New operations can be added almost anywhere in the tree however adding them to the leaf means we keep it as close to the data. Only some leaves may require this new operation in which case the changes are not pervasive through out the expression tree. This is especially helpful given that the expression could be used anywhere, nested and recursive. The size of data used and the size of the tree can be arbitrarily large, so considering performance is helpful. Query works similarly except that the expression can be part of the predicate in a query.  Predicate push down allows query to be passed through different systems. The servers typically don't interpret what the expression is, if it's user defined and operates on their data. For the ones that the server needs to keep track of, these expressions are compiled and have an execution plan. Execution plan helps to improve and control execution because the expressions are translated into a language that the system can work on. Query and Expressions have their purpose and are often interchangeable and there are usually many ways to solve a problem using either or both.  You can traverse the expression tree with an expression tree visitor.
Queries when they conform to the conventions that LINQ proposes can be executed by more than one systems such as the Entity Framework and the database server. LINQ is Language integrated queries and it defines queries in a way that can be executed against different data stores such as XML, Database server, ado.net datasets etc. These queries typically take the form of standard query operator methods such as Where, Select, Count, Max and such others. Typically LINQ queries are not executed until the query variable is iterated over. This is why we use Lambdas  Queries are generally more readable than their corresponding method syntax. IQueryable queries are compiled to expression trees while the IEnumerable queries are compiled to the delegates.  The compilers provide support to parse the lambdas in the statement. The LINQ expressions have a compile method that compiles the code represented by an expression tree into an executable delegate. There is an expression tree viewer application in the Visual Studio samples.
LINQ queries make the queries part of the programming constructs available in a language while they hide the data that they operate on. In this case, it is important to mention that different data sources may have different requirements or syntax for expressing their queries. LINQ to XML for example may need the XML queries be written in XPATH. This is different from the relational queries which are more like the LINQ constructs themselves. Queries against any data store can be captured and replayed independent of the caller that makes these queries.
LINQ queries and expressions that have Lambdas have the benefit that the Lambdas are evaluated only when the results are needed.