The intersection of two sets is the set of elements that are common to both sets.  

For example if we have two sets A = {1, 2, 3} and B = {2, 3, 4}, the intersection is {2, 3}, since this are the elements that are present in both sets.
The set class defines the intersection() method which returns a new set that is the intersection of the current set an another set(s)  given as argument.

ExampleEdit & Run

Using intersection() 

set1 = {1, 2, 3, 4, 5}
set2 = {3, 4, 5, 6, 7}

result = set1.intersection(set2)
print(result)
 Visualize 
Output:
{3, 4, 5}

[Finished in 0.018367443000897765s]

As you can see from the above example, the set.intersection method creates a new set with the common elements of both sets.

The set.intersection_update() method 

Unlike the intersection() method, the intersection_update() method does not create a new set. It instead modifies the existing set by removing all elements that are not present in both sets.

Syntax:
set1.intersection_update(set2, ...)

Note: Multiple iterables may be given as arguments.

The method, removes elements from set1 that are not common to both set1 and set2.

ExampleEdit & Run

Using intersection-update()

set1 = {1, 2, 3, 4, 5}
set2 = {3, 4, 5, 6, 7}

set1.intersection_update(set2) #modifies set1
print(set1)
 Visualize 
Output:
{3, 4, 5}

[Finished in 0.020710433833301067s]

passing multiple sets/iterables

The intersection_update(), allows multiple iterables(not just sets) to be passed as arguments. Similarly, it modifies the current sets by removing the elements that are not common in all the iterables.

ExampleEdit & Run
set1 = {1, 2, 3, 4, 5}
set2 = [3, 4, 5, 6, 7] # a list
set3 = (4, 5, 6, 7)

set1.intersection_update(set2, set3) #modifies set1
print(set1)
 Visualize 
Output:
{4, 5}

[Finished in 0.025424996856600046s]

Using the &= operator instead 

The &= is the operator version of the intersection_update() method. However, with this approach, the argument must be set not just any iterable.

Syntax:
set1 &= set2

The operator removes the elements in set1 that are not common to both set1 and set2.

ExampleEdit & Run
set_a = {'A', 'B', 'C', 'D'}
set_b = {'A', 'C', 'E', 'F'}

set_a &= set_b
print(set_a)#set_a is modified
 Visualize 
Output:
{'C', 'A'}

[Finished in 0.026063458062708378s]