What is the importance of Rcon in Rjindael's key expansion from a security prespective? I do not see why the Rcon function is important, it looks like a waste of cycles.

$$\operatorname{Rcon}(i) = 2^{i-1} \bmod p(x)$$ is in  $\operatorname{GF}(2^8)$, where $p(x)$ is the irreducible polynomial $x^8+x^4+x^3+x+1$.
According to Section 3.8 of "The Design of Rijndael", authored by the cipher's creators, the purpose is to eliminate symmetries in the key schedule:


  The non-linear function is realized by means of the application of $\mathrm S_\mathrm{RD}$ to the four bytes of the column, an additional cyclic rotation of the bytes within the column and the addition of a round constant (for elimination of symmetry). The round constants are independent of $\mathrm N_\mathrm k$, and defined by a recursion rule in $\operatorname{GF}(2^8)$:


(Emphasis mine.)

Section 5.8 elaborates a bit more on this:


  For the key schedule in Rijndael the criteria are less ambitious. Basically, the key schedule is there for three purposes.
  
  
  The first one is the introduction of asymmetry. Asymmetry in the key schedule prevents symmetry in the round transformation and between the rounds leading to weaknesses or allows attacks. Examples of such weaknesses are the complementation property of the DES or weak keys such as in the DES [28]. Examples of attacks that exploit symmetry are slide attacks.
  


(Emphasis mine.)

To summarize: Adding the round constants $\mathrm{Rcon}$ is a very cheap way (it's not that many cycles) to make each step of the key schedule slightly different, avoiding a variety of attacks that have become apparent in the past.