Checkpoint is an internal process that writes all dirty pages (modified pages) from Buffer Cache to Physical disk, apart from this it also writes the log records from log buffer to physical file. Writing of Dirty pages from buffer cache to data file is also known as Hardening of dirty pages. It is a dedicated process and runs automatically by SQL Server at specific intervals. SQL Server runs checkpoint process for each Database individually.
Operation that occur when checkpoint is issued
1) All dirty data file pages for the database are written to disk (all pages that have changed in memory since they were read from disk or since the last checkpoint), regardless of the state of the transaction that made the change.
2) Before a page is written to disk, all log records up to and including the most recent log record describing a change to that page are written to disk. This guarantees recovery can work and is called write-ahead logging. Log records are written to the log sequentially, and log records from multiple transactions will be interspersed in the log. The log cannot be selectively written to disk, so writing a dirty page to disk that only has a single log record affecting it may mean writing many more previous log records to disk as well.
3) Log records describing the checkpoint are generated.
4) The LSN of the checkpoint is recorded in the database boot page in the dbi_checkptLSN field
5) If in the SIMPLE recovery model, the VLFs in the log are checked to see whether they can be marked inactive (called clearing or truncating the log – both of which are terrible misnomers, as nothing is either physically cleared or truncated).

Four types of Checkpoints:
Automatic: This is the most common checkpoint which runs as a process in the background to make sure SQL Server Database can be recovered in the time limit defined by the Recovery Interval – Server Configuration Option.

Indirect: This is new in SQL Server 2012. This also runs in the background but to meet a user-specified target recovery time for the specific Database where the option has been configured. Once the Target_Recovery_Time for a given database has been selected this will override the Recovery Interval specified for the server and avoid Automatic Checkpoint on such DB.

Manual: This one runs just like any other T-SQL statement, once you issue checkpoint command it will run to its completion. Manual Checkpoint runs for your current Database Only. You can also specify the Checkpoint_Duration which is optional, this duration specifies the time in which you want your checkpoint to complete.

Internal: As a user you can’t control Internal Checkpoint. Issued on specific operations such as:
1. Shutdown initiates a Checkpoint operation on all databases except when Shutdown is not clean (Shutdown with nowait)
2. If the recovery model gets changed from Full\Bulk-logged to Simple.
3. While taking Backup of the Database.
4. If your DB is in Simple Recovery model, checkpoint process executes automatically either when the log becomes 70% full, or based on Server option-Recovery Interval.
5. Alter Database command to add or remove a data\log file also initiates a checkpoint.
6. Checkpoint also takes place when the recovery model of the DB is Bulk-Logged and a minimally logged operation is performed.
7. DB Snapshot creation.