Manipulatives are any object you can physically use to support the learning of maths, there are loads out there!
Often the use of manipulatives is seen in Primary education or when a student is struggling with something but over recent years I have found embedding this into regular practice successful. Yes they can help learners with 'learning to count' but they can also range up to learners 'completing the square' and more complex maths.
Manipulatives are generally used when introducing a topic and stay around until learners feel they no longer need them. A popular approach is known as CPAL (Concrete, Pictorial, Abstract language), this as suggested moves from using manipulatives then to drawing pictures/diagrams to abstract calculations.
I would recommend looking at CPD for using specific manipulatives but there is a whole range of stuff online too, just going onto Youtube would give you an nice introduction. My personal favourite is algebra tiles, the versatility is amazing. I also think two-colour or double sided counters are very good. The amount of times learners make mistakes with negative numbers is astonishing, with double sided counters the hope would to embed learning and increase understanding to then be able to access the deeper maths.
Jonny Hall has also created a wide range of online versions on MathsBot to use alongside or as an alternative.