Q:

What are uses of cookies in web apps? 

I am building a web app and have noticed that other web apps (gmail in particular) use cookies and it logs you out if you don't have cookies enabled.  Any idea what these cookies are used for that they are so crucial?  Are there any common uses for cookies in web apps? 

A:

It enables the server to maintain a client-specific state across requests (session) in the server side.  It also enables JavaScript to maintain a client-specific state across requests in the client side without need for server interaction. 

A:

A cookie is a small piece of data (name-value pair) sent from a website (sever side) and stored in a user's web browser while the user is browsing that website.  Cookies were designed to provide stateful information about user interaction in spite the stateless nature of HTTP protocol.  Cookies can be categorised based on its nature. 
Types of cookie can be selected based on the capabilities you want the cookie to have. 
Session cookie
A session cookie, also known as an in-memory cookie or transient cookie, exists only in temporary memory, while the user navigates the website. ( In java, Session cookie can be created by calling getSession() on request object).  Web browsers normally delete session cookies when the user closes the browser.  This type of cookies may be used to maintain data related to the user during navigation but in the same session.  User can go back and forth on website without affecting the preferences but the moment browser is shut down or session timeout, all preferences will be lost. 
Persistent cookie
A persistent cookie outlasts user sessions if you does not set the max-age.  To retain the cookie beyond the user session, you have to set Max-Age for that cookie.  Cookie must have data (name-value pair) which will sent back to the server every time the user visited the website.  This could be used to record a vital piece of information such as how the user initially came to this website or the preferences made etc.  Persistent cookies may be used to maintain data related to the user during navigation, possibly across multiple visits in different time.  Persistent cookies store user related data which will be used for future visit to website.  Persistent cookie can be used as shopping cart to which users can store items they want to purchase as they navigate throughout the site or in future. 
Secure cookie
A secure cookie has the secure attribute enabled and is only used via HTTPS, ensuring that the cookie is always encrypted when transmitting from client to server.  This makes the cookie less likely to be exposed to cookie theft via eavesdropping.  In addition to that, all cookies are subject to browser's same-origin-policy.  
As you asked about Gmail cookie mechanism, yes Gmail is using this secure cookie mechanism to store username and random token as your credentials to login.  Yes, it is not storing your original password in secure cookie instead when you successfully enter the correct username and password and say yes to remember my password, it generates a random number (token) for your username as a login cookie issued in addition to the standard session management cookie and store username and random number as password in its database.  That cookie cannot be used by other device as it is using same-origin-policy.  The username and token are stored as a pair in a database table.  When a user again visits the site, the login cookie will be sent to the server in the request object automatically from browser, then the username and token are verified in the database by the server.  If the pair is present, the user is considered authenticated.  The used token is removed from the database.  A new token is generated and stored in database with the username, and issued to the user via a new login cookie in the response object.  If the pair is not present, the login cookie is ignored.  Users entered via this mechanism are not permitted to access certain protected information or functions such as changing a password, viewing Personally Identifiable Information (PII).  To perform those operations, the user must first successfully submit a normal username/password login form which will pop automatically when you tried to do these prohibited operations.  Since this approach allows the user to have multiple remembered logins from different browsers or computers. 
HttpOnly cookie
The HttpOnly attribute is supported by most modern browsers.  On a supported browser, an HttpOnly session cookie will be used only when transmitting HTTP (or HTTPS) requests, thus restricting access from other non-HTTP APIs such as JavaScript.  This restriction mitigates but does not eliminate the threat of session cookie theft via cross-site scripting (XSS).  This feature applies only to session-management cookies and not on other browser cookies. 
Third-party cookie
Third-party cookies are cookies that belong to domains different from the one shown in the address bar.  It is mostly used for advertisement by keeping tracks of user preferences and browser history to judge its inclination and sell him something accordingly.