Can someone explain what 'centralized validation' really means

[BNO]

on the official wallet choosing page:
https://bitcoin.org/en/choose-your-wallet

It says about mycelium under the point "centralized validation":

This wallet relies on a centralized service by default. This means a third party must be trusted to not hide or simulate payments.

What does this mean, the third party i assume is mycelium. How secure is this?

[AgentofCoin]

Your wallet choice really depends on what you wish to do and how much you wish to hold/store.
Mycelium is a mobile wallet and is good for small funds (spending btc).
Electrum is not mobile and is good for all funds, in theory (savings account).

With Mycelium (single server),

All thin clients ...[Ex. Mycelium]... currently connect to a single server, and are vulnerable to an attack similar to a double-spend. The attack can be run by that single server - the server can just lie to them that they received a Bitcoin transaction, and they, assuming the server does not lie, perform some service, transfer funds or send goods without actually receiving any Bitcoin in exchange. Therefore, they are implicitly trusting it.

With Electrum (SPV Client),

Electrum fetches blockchain information from Electrum servers, bitcoin nodes that index the blockchain by address. Electrum performs Simple Payment Verification to check the transactions returned by servers. For this, it fetches blokchain headers from about 10 random servers. In addition, Electrum servers are authenticated by SSL, in order to protect users from MITM attacks.

This is the link where I got the two above quotes:
https://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29_Clients

I am no expert and I hope this answers your question basically.

[stuff0577]

To OP: "Centralize Validation" means there is an authority which controls every valid transaction that are happening in the network. 

[BNO]

Hey forgot to write back: Thanks for that cool link man. Understand it now a little better.