How do catalysts provide alternative routes for reactions?
So catalysts provide an alternative pathway by allowing a new intermediate to be formed. 
For example consider the reaction of $A$ and $B$ to form $C$. this means that
$$\ce{A + B -&gt; C}$$
Say this reaction has  an activation energy of $x$ $kJmol^{-1}$. 

This reaction could also be possible with a catalyst $X$. This means that a new possible route for the reaction could be (there a multiple routes the new reaction could take this is just a simple example):
$$\ce{A + X-&gt;AX}$$ 
$$\ce{AX + B-&gt;C +X}$$
Now you have ended up in the same position using a catalyst and when not using a catalyst, seen as you add both reaction and cancel out common species then you get back to the equation of:
$$\ce{A + B -&gt; C}$$
These two reactions with the catalyst will have their own activation energies. Say these two reactions have activation energies $\pu{p}$ and $\pu{q}$ $\pu{kJmol^{-1}}$ and that $\pu{p&gt;q}$ (doesn't matter if $\pu{p}$ applies to the first or second reaction) then if $x&gt;p$ a particle needs less energy to proceed via the route with the catalyst compared to the route without the catalyst. 

As a particle now needs less energy for the product $\pu{C}$ to be formed, more particles will now be able to take part in the reaction thus increasing the amount of successful collisions per second which is the same in an increase in rate. This can be seen nicely in a general Maxwell-Boltzmann distribution of molecular energies as the new route will mean there's a lower activation energy overall meaning a lot more particles can react.