Please check below post for with and without sharing
1) https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_classes_keywords_sharing.htm

The with sharing keyword allows you to specify that the sharing rules for the current user be taken into account for a class. You have to explicitly set this keyword for the class because Apex code runs in system context. In system context, Apex code has access to all objects and fields— object permissions, field-level security, sharing rules aren’t applied for the current user. This is to ensure that code won’t fail to run because of hidden fields or objects for a user. The only exceptions to this rule are Apex code that is executed with the executeAnonymous call and Chatter in Apex. executeAnonymous always executes using the full permissions of the current user
 

public with sharing class sharingClass {

// Code here

}

Use the without sharing keywords when declaring a class to ensure that the sharing rules for the current user are not enforced. For example, you may want to explicitly turn off sharing rule enforcement when a class acquires sharing rules when it is called from another class that is declared using with sharing.

public without sharing class noSharing {

// Code here

}

Please check below post for sharing rule
1) http://amitsalesforce.blogspot.com/2016/02/types-of-sharing-in-salesforce.html

1. Force.com Managed Sharing
Force.com managed sharing involves sharing access granted by Force.com based on record ownership, the role hierarchy, and sharing rules:

• 1.1 Record Ownership :- Each record is owned by a user or optionally a queue for custom objects, cases and leads. The record owner is automatically granted Full Access, allowing them to view, edit, transfer, share, and delete the record.
• 1.2 Role Hierarchy :- The role hierarchy enables users above another user in the hierarchy to have the same level of access to records owned by or shared with users below. Consequently, users above a record owner in the role hierarchy are also implicitly granted Full Access to the record, though this behavior can be disabled for specific custom objects. The role hierarchy is not maintained with sharing records. Instead, role hierarchy access is derived at runtime. For more information, see “Controlling Access Using Hierarchies” in the Salesforce online help.
• 1.3 Sharing Rules :-Sharing rules are used by administrators to automatically grant users within a given group or role access to records owned by a specific group of users. Sharing rules cannot be added to a package and cannot be used to support sharing logic for apps installed from Force.com AppExchange. Sharing rules can be based on record ownership or other criteria. You can't use Apex to create criteria-based sharing rules. Also, criteria-based sharing cannot be tested using Apex. All implicit sharing added by Force.com managed sharing cannot be altered directly using the Salesforce user interface, SOAP API, or Apex.

2. User Managed Sharing, also known as Manual Sharing
User managed sharing allows the record owner or any user with Full Access to a record to share the record with a user or group of users. This is generally done by an end-user, for a single record. Only the record owner and users above the owner in the role hierarchy are granted Full Access to the record. It is not possible to grant other users Full Access. Users with the “Modify All” object-level permission for the given object or the “Modify All Data” permission can also manually share a record. User managed sharing is removed when the record owner changes or when the access granted in the sharing does not grant additional access beyond the object's organization-wide sharing default access level.

3. Apex Managed Sharing
Apex managed sharing provides developers with the ability to support an application’s particular sharing requirements programmatically through Apex or the SOAP API. This type of sharing is similar to Force.com managed sharing. Only users with “Modify All Data” permission can add or change Apex managed sharing on a record. Apex managed sharing is maintained across record owner changes.
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