There's a lot going on here. First, on line 46 we begin defining our insert statement. We create a string variable called select and make it equal to a SQL insert. If you know SQL, this is just a basic insert statements. This isn't a SQL tutorial so I'm not going to dissect it.
On line 50 I define another string called connectionString. This is a string used to connect to our SQL server. For a list of various connection strings, check out this very informative site: connectionstrings.com. You'll see my data source (the server name, basically) is localhost, 1433. This means I'm connecting to localhost (the local computer) on port 1433. The initial catalog is Guestbook. This is the database on this machine I'm connecting to. The userid is sa and the password is the password I set for that account.
You may wonder why it's set to localhost. In this case our sql server and web server is on the same computer, so that works fine. When a user connects to the web server to pull a web page, the web server connect to the SQL server to get data. The user never connects directly to the SQL server. If your SQL server were on a different computer from the web server, instead of localhost you'd need the ip or hostname of the SQL server.
On the next line I create an OleDbConnection object called conn and set it to be a new OleDbConnection. I pass the connectionString into this. Just like I created a string earlier by using string ip = ..., I created an OleDbConnection call conn using OleDbConnection conn = new OleDbConnection(connectionString);. This method allows me to pass in connectionString to tell OleDbConnection what to connect to. If you're not too clear on this part, don't worry. Just be aware that you need to do this to establish a database connection. As your knowledge of C# improves things like this will start to make more sense.
On line 53 I do conn.Open(). Remember on line 52 we defined conn as being the connection to the database. By using conn.Open(), we're opening the connection. Next on line 54 we're creating a new OleDbCommand called cm. To this we're passing the variables select (which is our insert statement) and conn (which is our database connection). This basically takes our insert statement we defined above and matches it up with our database connection.
On line 55 we create another new object, this one is an OleDbDataReader object called dr. This is created by taking our OleDbCommand object (cm) and using the ExecuteReader() method. This basically causes our SQL statement to be executed. On line 57 we then take our OleDbDataReader object and dispose of it (basically flush the memory usage) and finally on line 58 we close our database connection.