Ajedrez means 'chess'. It's a fantastic and uncommon word to find in a romantic pop song, which makes it very memorable.
Alejandro Sanz uses it in a clever and beautiful metaphor: "Si tú eres mi reina, gano al ajedrez" (If you are my queen, I win at chess). He's comparing life and love to a game of chess, saying that having her as his 'queen' guarantees his victory in the game of life.
This song is all about taking control of your love life and not waiting for fate to decide. Alejandro Sanz is tired of playing games and leaving things to chance. He tells his love interest straight up, "Si existe algún riesgo de verme sin ti / Yo no quiero apostar" (If there's any risk of seeing myself without you / I don't want to bet). He's completely smitten, saying he can't get her scent off him "Ni con todo el café de Colombia" (Not even with all the coffee in Colombia), which is a fun little nod to his duet partner, Shakira.
The whole vibe is urgent and a little impatient. The chorus is a direct command: "No lo pienses tanto y bésame" (Don't think so much and kiss me). They want to stop the uncertainty and move forward with "Cero miedo" (Zero fear). The best line has to be when they invite their partner to take charge of the relationship: "Mejor ven, pásate al volante" (Better come, get behind the wheel). It's a powerful way to say, "Let's do this together, right now."