There is a large linguistic trace left in the present day Spanish lexicon. The most obvious examples are the many Spanish words that begin with 'al', like algodon, alcalde, and almohada (cotton, mayor, and pillow). The Arabic word, along with the article 'al', was used to form a new word in Spanish.

The extent of the linguistic transfer differs depending on the length of Moorish control of an area. Southern areas like Andalusia will have a higher percentage of the lexicon composed of words with Arabic origins, while northern areas are more likely to use words with Romance origins.

The influences can be seen in many aspects of Spanish culture. The linguistic trace mentioned by /u/thenameoftherows is one. You can also see the influence is Spanish cuisine. The most notable gastronomic influence is in pastry. Most southern sweet dishes are made of nuts, honey and sesame seeds, pestiños being a great example. You can see similar Moroccan pastry in briwat. Another great influence was in architecture. There are still a lot of Islamic palaces and mosques in Spain, La Alhambra, The Cathedral-Mosque of Cordoba and Los Reales Alcazares in Seville being some of the most notable ones. I should also add that this influence is much more notorious in the southern regions of Spain, basically because the Islamic rule was longer.

The heaviest influence of arabic on spanish language was in agriculture. The arabs were highly skilled farmers and introduced to Spain (and later to Europe) several crops hitherto unknown like oranges, rice, cotton and others. Because of that, most of the words for fruits and vegetables in spanish are very different than the ones in other roman languages like french or italian. Example: peach/melocotón, apricot/albaricoque, orange/naranja, cotton/algodón, etc..